Equation 677 Database

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Magma e1ddb15d88ca…

magma e1ddb15d88ca
Size
705
Isomorphism class hash
e1ddb15d88ca6f791bed1f9e5fcf45a6f454d765ca713c2fef9b96f982b04e57
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 16:35:05
Display reorder
660,265,562,72,14,166,263,563,70,12,164,264,564,71,13,165,565,261,68,17,169,566,262,69,15,167,567,260,67,16,168,256,560,78,20,161,254,561,76,18,162,255,559,77,19,163,556,259,74,23,160,557,257,75,21,158,558,258,73,22,159,662,667,670,663,152,502,447,435,196,153,503,448,436,194,154,504,449,437,195,505,155,450,438,199,506,156,451,439,197,507,157,452,440,198,150,500,445,433,202,151,501,446,434,200,149,499,444,432,201,496,146,441,429,205,497,147,442,430,203,498,148,443,431,204,686,685,688,687,131,471,380,193,62,132,472,381,191,63,133,473,382,192,61,474,130,383,189,65,475,128,384,190,66,476,129,385,188,64,122,469,378,184,60,123,470,379,182,58,124,468,377,183,59,465,125,374,187,56,466,126,375,185,57,467,127,376,186,55,666,669,668,664,235,339,416,404,104,233,340,417,405,105,234,338,418,406,103,342,231,419,407,107,343,232,420,408,108,341,230,421,409,106,241,345,414,402,110,239,346,415,403,111,240,344,413,401,109,348,237,410,398,113,349,238,411,399,114,347,236,412,400,112,675,677,673,676,139,580,392,581,356,137,583,393,582,357,138,585,394,584,358,586,135,395,587,359,589,136,396,588,360,591,134,397,590,361,145,576,390,577,354,143,579,391,578,355,144,574,389,575,353,569,141,386,568,350,571,142,387,570,351,573,140,388,572,352,672,661,671,665,225,332,180,514,246,226,333,181,515,247,224,334,179,516,245,335,228,176,517,242,336,229,177,518,243,337,227,178,519,244,223,330,171,512,252,221,331,172,513,253,222,329,170,511,251,326,219,174,508,248,327,220,175,509,249,328,218,173,510,250,695,697,694,693,102,483,115,428,48,100,643,642,640,641,101,647,644,645,646,651,98,649,648,650,655,99,653,652,654,659,97,657,656,658,93,478,121,423,52,91,479,119,424,53,92,477,120,422,54,481,96,117,426,51,482,94,118,427,49,480,95,116,425,50,702,701,703,704,26,538,37,628,629,24,539,38,630,631,25,540,36,632,633,541,29,40,634,635,542,27,41,636,637,543,28,39,638,639,32,536,43,625,624,30,537,44,627,626,31,535,42,623,622,532,35,46,617,616,533,33,47,619,618,534,34,45,621,620,699,700,696,698,216,604,605,368,526,217,606,607,369,527,215,608,609,370,528,610,212,611,371,529,612,213,613,372,530,614,214,615,373,531,207,601,600,366,524,208,603,602,367,525,206,599,598,365,523,593,210,592,362,520,595,211,594,363,521,597,209,596,364,522,674,680,684,683,83,269,490,550,459,84,270,491,551,460,82,271,492,552,461,268,79,493,553,462,266,80,494,554,463,267,81,495,555,464,89,275,488,548,457,90,276,489,549,458,88,277,487,547,456,274,85,484,544,453,272,86,485,545,454,273,87,486,546,455,682,678,681,679,6,293,313,319,289,7,294,311,317,287,8,295,312,318,288,292,9,309,315,285,290,10,310,316,286,291,11,308,314,284,4,299,304,325,280,5,300,302,323,278,3,301,303,324,279,298,1,307,321,283,296,0,305,322,281,297,2,306,320,282,690,689,692,691 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#357eb5a07f294d712e4efb5d2eb529ba387854e51bbe679ac1cbb62e1e3b2fae, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 16:35:06 · history